In this paper we present the modelling of elastic intra-species electron-electron and inter-species electron-ion scattering in a plasma on the basis of the Fokker-Planck collision operator. Taking into account the equivalence of this operator with a stochastic differential equation, we propose a Particle-in-Cell based approach for the numerical solution of the Fokker-Planck collision term. As we will see, the introduced numerical concept allows the simulation of the collisional relaxation process in a fully self-consistent fashion.

The energetic optimization problem, e.g., searching for the optimal switching protocol of certain system parameters to minimize the input work, has been extensively studied by stochastic thermodynamics. In this work, we study this problem numerically using iterative dynamic programming. The model systems under investigation are toy actuators consisting of spring-linked beads with loading force imposed on both ending beads. For the simplest case, i.e., a one-spring actuator driven by tuning the stiffness of the spring, we compare the optimal control protocol of the stiffness for both the overdamped and the underdamped situations, and discuss how inertial effects alter the irreversibility of the driven process and thus modify the optimal protocol. Then, we study the systems with multiple degrees of freedom by constructing oligomer actuators, in which the harmonic interaction between the two ending beads is tuned externally. With the same rated output work, actuators of different constructions demand different minimal input work, reflecting the influence of the internal degrees of freedom on the performance of the actuators.

Despite decades of development, Lagrangian hydrodynamics of strength-free materials presents numerous open issues, even in one dimension. We focus on the problem of closing a system of equations for a two-material cell under the assumption of a single velocity model. There are several existing models and approaches, each possessing different levels of fidelity to the underlying physics and each exhibiting unique features in the computed solutions. We consider the case in which the change in heat in the constituent materials in the mixed cell is assumed equal. An instantaneous pressure equilibration model for a mixed cell can be cast as four equations in four unknowns, comprised of the updated values of the specific internal energy and the specific volume for each of the two materials in the mixed cell. The unique contribution of our approach is a physics-inspired, geometry-based model in which the updated values of the sub-cell, relaxing-toward-equilibrium constituent pressures are related to a local Riemann problem through an optimization principle. This approach couples the modeling problem of assigning sub-cell pressures to the physics associated with the local, dynamic evolution. We package our approach in the framework of a standard predictor-corrector time integration scheme. We evaluate our model using idealized, two material problems using either ideal-gas or stiffened-gas equations of state and compare these results to those computed with the method of Tipton and with corresponding pure-material calculations.

Three-dimensional molecular dynamics (MD) simulations of gas flows con- fined within nano-scale channels are investigated by introduction of a smart wall model that drastically reduces the memory requirements of MD simulations for gas flows. The smart wall molecular dynamics (SWMD) represents three-dimensional FCC walls using only 74 wall molecules. This structure is kept in the memory and utilized for each gas molecule surface collision. Linear Couette flow of argon at Knudsen number 10 is investigated using the SWMD utilizing Lennard-Jones potential interactions. Effects of the domain size on the periodicity boundary conditions are investigated using three-dimensional simulations. Domain sizes that are one mean-free-path long in the periodic dimensions are sufficient to obtain domain-size independent MD solutions of nano-scale confined gas flows. Comparisons between the two- and three-dimensional simulations show the inadequacy of two-dimensional MD results. Three-dimensional SWMD simulations have shown significant deviations of the velocity profile and gas density from the kinetic theory based predictions within the force penetration region of the walls.

In this paper, accurate and efficient simulation of cell motion in a biological fluid flow is investigated. The membrane of a moving cell is represented by a thin shell composed of incompressible neo-Hookean elastic materials and the liquids around the membrane are approximated as incompressible Newtonian flows with low Reynolds numbers. The biofluid mechanics is approximated by the Stokes flow equations. A low-order BEM model is developed for the two biological fluids coupled at the membrane surface. The moving boundary problem in fluid mechanics can be effectively solved using the BEM with a GMRES solver. The FEM model based on a flat thin shell element is further developed to predict the membrane load due to the large deformation of a moving cell. Computational efficiency is greatly improved due to the one-dimensional reduction in the present BEM and FEM models. The BEM solver for the biological fluids is coupled with the FEM solver for the cell membrane at the membrane surface. The position of the membrane surface nodes is advanced in time by using the classical fourth-order Runge-Kutta method. Numerical instability is avoided by using a relatively small time step. Further numerical instabilities in the FEM solver is alleviated by using various techniques. The present method is applied to the FSI problems of cell motion in a cylindrical flow. Numerical examples can illustrate the distinct accuracy, efficiency and robustness of the present method. Furthermore, the importance of bending stiffness of a cell membrane for stable cell motion simulation is emphasized. It is suggested that the present approach be an appealing alternative for simulating the fluid-structure interaction of moving cells.

In this paper, we propose a weighted Runge-Kutta (WRK) method to solve the 2D acoustic and elastic wave equations. This method successfully suppresses the numerical dispersion resulted from discretizing the wave equations. In this method, the partial differential wave equation is first transformed into a system of ordinary differential equations (ODEs), then a third-order Runge-Kutta method is proposed to solve the ODEs. Like the conventional third-order RK scheme, this new method includes three stages. By introducing a weight to estimate the displacement and its gradients in every stage, we obtain a weighted RK (WRK) method. In this paper, we investigate the theoretical properties of the WRK method, including the stability criteria, numerical error, and the numerical dispersion in solving the 1D and 2D scalar wave equations. We also compare it against other methods such as the high-order compact or so-called Lax-Wendroff correction (LWC) and the staggered-grid schemes. To validate the efficiency and accuracy of the method, we simulate wave fields in the 2D homogeneous transversely isotropic and heterogeneous isotropic media. We conclude that the WRK method can effectively suppress numerical dispersions and source noises caused in using coarse grids and can further improve the original RK method in terms of the numerical dispersion and stability condition.

Based on the recent development in shallow flow modelling, this paper presents a finite volume Godunov-type model for solving a 4×4 hyperbolic matrix system of conservation laws that comprise the shallow water and depth-averaged solute transport equations. The adopted governing equations are derived to preserve exactly the solution of lake at rest so that no special numerical technique is necessary in order to construct a well-balanced scheme. The HLLC approximate Riemann solver is used to evaluate the interface fluxes. Second-order accuracy is achieved using the MUSCL slope limited linear reconstruction together with a Runge-Kutta time integration method. The model is validated against several benchmark tests and the results are in excellent agreement with analytical solutions or other published numerical predictions.

Electrowetting has been proposed as a technique for manipulating droplets surrounded by air or oil. In this paper, we discuss the modeling and simulation of the droplet fission process between two parallel plates inside an electrowetting on dielectric (EWOD) device. Since the gap between the plates is small, we use the two-phase Hele-Shaw flow as a model. While there are several high order methods around, such as the immersed interface methods [1, 2], we decide to use two first-order methods for simplicity. A ghost-fluid (GF) method is employed to solve the governing equations and a local level set method is used to track the drop interface. For comparison purposes, the same set of two-phase Hele-Shaw equations are also solved directly using the immersed boundary (IB) method. Numerical results are consistent with experimental observations reported in the literature.

A combined lattice Boltzmann and discrete element approach is proposed for numerical modelling of magnetorheological fluids. In its formulation, the particle dynamics is simulated by the discrete element method, while the fluid field is resolved with the lattice Boltzmann method. The coupling between the fluid and the particles are realized through the hydrodynamic interactions. Procedures for computing magnetic, contact and hydrodynamic forces are discussed in detail. The applicability of the proposed solution procedure is illustrated via a two-stage simulation of a MR fluid problem with four different particle volume fractions. At the first stage, simulations are performed for the particle chain formation upon application of an external magnetic field; and at the second stage, the rheological properties of the MR fluid under different shear loading conditions are investigated with the particle chains established at the first stage as the initial configuration.

In this article we report the release of a new program for calculating emissivity and other physical parameters in atomic transition processes. The program, which can be downloaded with its documentation and a sample of input and output files from www.scienceware.net/id1.html, passed various rigorous tests and was used alongside R-matrix and Autostructure codes to generate theoretical data and analyze observational data. It is particularly useful for investigating atomic transition lines in astronomical context as the program is capable of generating a huge amount of theoretical data and comparing it to observational line list. A number of atomic transition algorithms and analytical techniques are implemented within the program and can be very useful in various situations. The program can be described as fast and efficient. Moreover, it requires modest computational resources.